Solve 1-11/x+28/x^2/1-frac{9{x}+14/x^2}

$$\frac { 1 - \frac { 11 } { x } + \frac { 28 } { x ^ { 2 } } } { 1 - \frac { 9 } { x } + \frac { 14 } { x ^ { 2 } } }$$

Evaluate

$$\frac{x-4}{x-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x}{x}-\frac{11}{x}+\frac{28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

Since \frac{x}{x} and \frac{11}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-11}{x}+\frac{28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-11}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x-11\right)x}{x^{2}}+\frac{28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

Since \frac{\left(x-11\right)x}{x^{2}} and \frac{28}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(x-11\right)x+28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

Do the multiplications in \left(x-11\right)x+28.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{x}{x}-\frac{9}{x}+\frac{14}{x^{2}}}$$

Since \frac{x}{x} and \frac{9}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{x-9}{x}+\frac{14}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-9}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{\left(x-9\right)x}{x^{2}}+\frac{14}{x^{2}}}$$

Since \frac{\left(x-9\right)x}{x^{2}} and \frac{14}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{\left(x-9\right)x+14}{x^{2}}}$$

Do the multiplications in \left(x-9\right)x+14.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{x^{2}-9x+14}{x^{2}}}$$

Divide \frac{x^{2}-11x+28}{x^{2}} by \frac{x^{2}-9x+14}{x^{2}} by multiplying \frac{x^{2}-11x+28}{x^{2}} by the reciprocal of \frac{x^{2}-9x+14}{x^{2}}.

$$\frac{\left(x^{2}-11x+28\right)x^{2}}{x^{2}\left(x^{2}-9x+14\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}-11x+28}{x^{2}-9x+14}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x-4\right)}{\left(x-7\right)\left(x-2\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x-4}{x-2}$$

Expand

$$\frac{x-4}{x-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x}{x}-\frac{11}{x}+\frac{28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

Since \frac{x}{x} and \frac{11}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-11}{x}+\frac{28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-11}{x} times \frac{x}{x}.

$$\frac{\frac{\left(x-11\right)x}{x^{2}}+\frac{28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

Since \frac{\left(x-11\right)x}{x^{2}} and \frac{28}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\left(x-11\right)x+28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

Do the multiplications in \left(x-11\right)x+28.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{1-\frac{9}{x}+\frac{14}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{x}{x}-\frac{9}{x}+\frac{14}{x^{2}}}$$

Since \frac{x}{x} and \frac{9}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{x-9}{x}+\frac{14}{x^{2}}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{x-9}{x} times \frac{x}{x}.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{\left(x-9\right)x}{x^{2}}+\frac{14}{x^{2}}}$$

Since \frac{\left(x-9\right)x}{x^{2}} and \frac{14}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{\left(x-9\right)x+14}{x^{2}}}$$

Do the multiplications in \left(x-9\right)x+14.

$$\frac{\frac{x^{2}-11x+28}{x^{2}}}{\frac{x^{2}-9x+14}{x^{2}}}$$

Divide \frac{x^{2}-11x+28}{x^{2}} by \frac{x^{2}-9x+14}{x^{2}} by multiplying \frac{x^{2}-11x+28}{x^{2}} by the reciprocal of \frac{x^{2}-9x+14}{x^{2}}.

$$\frac{\left(x^{2}-11x+28\right)x^{2}}{x^{2}\left(x^{2}-9x+14\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{x^{2}-11x+28}{x^{2}-9x+14}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x-4\right)}{\left(x-7\right)\left(x-2\right)}$$

Cancel out x-7 in both numerator and denominator.

$$\frac{x-4}{x-2}$$